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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: Tính A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + =. + 1/ a(a+1)(a+2)

Tháng Mười 2, 2022 Toán học 1 Comment 0 views

Toán Lớp 7: Tính A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + …………. + 1/ a(a+1)(a+2)

Comments ( 1 )

  1. hienchaudiem
    hienchaudiem
    2 Tháng Mười, 2022 at 11:26 chiều
    Reply
     Ta có : A = 1/( 1 . 2 . 3 ) + 1/( 2 . 3 . 4 ) + 1/( 3 . 4 . 5 ) + ….. + 1/( a . ( a + 1 ) . ( a + 2 ) )
    A = ( 2/( 1 . 2 . 3 ) + 2/( 2 . 3 . 4 ) + 2/( 3 . 4 . 5 ) + ….. + 2/( a . ( a + 1 ) . ( a + 2 ) ) ) . 1/2
    Vì 2/( n . ( n + 1 ) . ( n + 2 ) ) = 1/( n . ( n + 1 ) ) – 1/( ( n + 1 ) . ( n + 2 ) )
    ⇒ 2/( 1 . 2 . 3 ) = 1/( 1 . 2 ) – 1/( 2 . 3 ) ; …… ; 2/( a . ( a + 1 ) . ( a + 2 ) ) = 1/( a . ( a + 1 ) ) – 1/( ( a + 1 ) . ( a + 2 ) )
    ⇒ A = ( 1/( 1 . 2 ) – 1/( 2 .  3 ) + 1/( 2 . 3 ) – 1/( 3 . 4 ) + 1/( 3 . 4 ) – 1/( 4 . 5 ) + …. + 1/( a . ( a + 1 ) ) – a/( ( a + 1 ) . ( a + 2 ) ) ) . 1/2
    A = ( 1/( 1 . 2 ) – 1/( ( a + 1 ) . ( a + 2 ) ) ). 1/2
    A = ( 1/2 – 1/( ( a + 1 ) . ( a + 2 ) ) ) . 1/2
    Vậy , A = ( 1/2 – 1/( ( a + 1 ) . ( a + 2 ) ) ) . 1/2

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222-9+11+12:2*14+14 = ? ( )

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